That's exactly what we did last year on a trip to Seattle - we packed shoes, pedals, and all our bike stuff in one suitcase ("real clothes" in another suitcase) then rented bikes from one of the local bike shops in the area.

I worried that our beloved bikes would get lost or broken if we took them on the plane. It really worked out; just be prepared for airport security to search your luggage....both ways! All that metal will set off their alarms

Lorie